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You can try below code for that

$collection = Mage::getModel('YourModel/ModelClass')->getCollection();
$collection->addFieldToFilter('updated_at''start_date', array('gteq' =>$first));
$collection->addFieldToFilter('updated_at''end_date', array('lteq' => $last));

You can try below code for that

$collection = Mage::getModel('YourModel/ModelClass')->getCollection();
$collection->addFieldToFilter('updated_at', array('gteq' =>$first));
$collection->addFieldToFilter('updated_at', array('lteq' => $last));

You can try below code for that

$collection = Mage::getModel('YourModel/ModelClass')->getCollection();
$collection->addFieldToFilter('start_date', array('gteq' =>$first));
$collection->addFieldToFilter('end_date', array('lteq' => $last));
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You can try below code for that

$collection = Mage::getModel('YourModel/ModelClass')->getCollection();
$collection->addFieldToFilter('updated_at', array('gteq' =>$first));
$collection->addFieldToFilter('updated_at', array('lteq' => $last));